Simple Elastic Network Model Research Articles

Allostery Explained Through Synchronized Oscillators and Fractal Networks

It is well known that emergent slow motions of proteins can be modeled by a simple elastic network model that treats amino acid residues as interconnected harmonic oscillators. It is also known that coupled oscillators synchronize if their internal frequencies are close enough with synchronization patterns being dependent on the topology of the network. Combining these concepts with the well-established fact that contacts in proteins are distributed in a fractal-like way, we consider a mechanistic model of dynamics driven allostery. One can argue that changes in oscillator synchronization define local entropic properties of the protein and can drive the protein slow dynamics. The short-range nature of the interactions that give rise to the emergent allosteric signaling phenomenon dictates that simple methods for the network description such as direct contacts or Local Spatial Pattern (LSP) alignment are preferable to more complicated computational tools such as Mutual Information.

Simple Elastic Network Models for Exhaustive Analysis of Long Double-Stranded DNA Dynamics with Sequence Geometry Dependence.

Simple elastic network models of DNA were developed to reveal the structure-dynamics relationships for several nucleotide sequences. First, we propose a simple all-atom elastic network model of DNA that can explain the profiles of temperature factors for several crystal structures of DNA. Second, we propose a coarse-grained elastic network model of DNA, where each nucleotide is described only by one node. This model could effectively reproduce the detailed dynamics obtained with the all-atom elastic network model according to the sequence-dependent geometry. Through normal-mode analysis for the coarse-grained elastic network model, we exhaustively analyzed the dynamic features of a large number of long DNA sequences, approximately ∼150 bp in length. These analyses revealed positive correlations between the nucleosome-forming abilities and the inter-strand fluctuation strength of double-stranded DNA for several DNA sequences.

Internal Normal Mode Analysis (iNMA) Applied to Protein Conformational Flexibility

We analyze the capacity of normal modes to predict observed protein conformational changes, and, notably, those induced by the formation of protein-protein complexes. We show that normal modes calculated in internal coordinate space (ICS) provide better predictions. For a large test set, using the ICS approach describes the conformational changes more completely, and with fewer low-frequency modes than the equivalent Cartesian coordinate modes, despite the fact that the internal coordinate calculations were restricted to torsional angles. This can be attributed to the fact that the use of ICS extends the range over which movements along the corresponding eigenvectors remain close to the true conformational energy hypersurface. We also show that the PaLaCe coarse-grain protein model performs better than a simple elastic network model. We apply ICS normal-mode analysis to protein complexes and, by extending the approach of Sunada and Go̅, [Sunada, S.; Go̅, N. J. Comput. Chem. 1995, 16, 328-336], we show that we can couple an accurate view of the Cartesian coordinate movements induced by ICS modes with the detection of the key residues responsible for the movements.

A mechanistic stress model of protein evolution accounts for site-specific evolutionary rates and their relationship with packing density and flexibility

BackgroundProtein sites evolve at different rates due to functional and biophysical constraints. It is usually considered that the main structural determinant of a site’s rate of evolution is its Relative Solvent Accessibility (RSA). However, a recent comparative study has shown that the main structural determinant is the site’s Local Packing Density (LPD). LPD is related with dynamical flexibility, which has also been shown to correlate with sequence variability. Our purpose is to investigate the mechanism that connects a site’s LPD with its rate of evolution.ResultsWe consider two models: an empirical Flexibility Model and a mechanistic Stress Model. The Flexibility Model postulates a linear increase of site-specific rate of evolution with dynamical flexibility. The Stress Model, introduced here, models mutations as random perturbations of the protein’s potential energy landscape, for which we use simple Elastic Network Models (ENMs). To account for natural selection we assume a single active conformation and use basic statistical physics to derive a linear relationship between site-specific evolutionary rates and the local stress of the mutant’s active conformation.We compare both models on a large and diverse dataset of enzymes. In a protein-by-protein study we found that the Stress Model outperforms the Flexibility Model for most proteins. Pooling all proteins together we show that the Stress Model is strongly supported by the total weight of evidence. Moreover, it accounts for the observed nonlinear dependence of sequence variability on flexibility. Finally, when mutational stress is controlled for, there is very little remaining correlation between sequence variability and dynamical flexibility.ConclusionsWe developed a mechanistic Stress Model of evolution according to which the rate of evolution of a site is predicted to depend linearly on the local mutational stress of the active conformation. Such local stress is proportional to LPD, so that this model explains the relationship between LPD and evolutionary rate. Moreover, the model also accounts for the nonlinear dependence between evolutionary rate and dynamical flexibility.

Epithelial and endothelial damage induced by mechanical ventilation modes

The adult respiratory distress syndrome (ARDS) is a common cause of respiratory failure with substantial impact on public health. Patients with ARDS generally require mechanical ventilation, which risks further lung damage. Recent improvements in ARDS outcomes have been attributed to reductions in deforming stress associated with lung protective mechanical ventilation modes and settings. The following review details the mechanics of the lung parenchyma at different spatial scales and the response of its resident cells to deforming stress in order to provide the biologic underpinnings of lung protective care. Although lung injury is typically viewed through the lens of altered barrier properties and mechanical ventilation-associated immune responses, in this review, we call attention to the importance of heterogeneity and the physical failure of the load bearing cell and tissue elements in the pathogenesis of ARDS. Specifically, we introduce a simple elastic network model to better understand the deformations of lung regions, intra-acinar alveoli and cells within a single alveolus, and consider the role of regional distension and interfacial stress-related injury for various ventilation modes. Heterogeneity of stiffness and intercellular and intracellular stress failure are fundamental components of ARDS and their development also depends on the ventilation mode.

Inferring a weighted elastic network from partial unfolding with coarse-grained simulations

A number of studies have demonstrated that simple elastic network models can reproduce experimental B-factors, providing insights into the structure-function properties of proteins. Here, we report a study on how to improve an elastic network model and explore its performance by predicting the experimental B-factors. Elastic network models are built on the experimental Cα coordinates, and they only take the pairs of Cα atoms within a given cutoff distance rc into account. These models describe the interactions by elastic springs with the same force constant. We have developed a method based on numerical simulations with a simple coarse-grained force field, to attribute weights to these spring constants. This method considers the time that two Cα atoms remain connected in the network during partial unfolding, establishing a means of measuring the strength of each link. We examined two different coarse-grained force fields and explored the computation of these weights by unfolding the native structures.

Flexible protein docking refinement using pose‐dependent normal mode analysis

Modeling conformational changes in protein docking calculations is challenging. To make the calculations tractable, most current docking algorithms typically treat proteins as rigid bodies and use soft scoring functions that implicitly accommodate some degree of flexibility. Alternatively, ensembles of structures generated from molecular dynamics (MD) may be cross-docked. However, such combinatorial approaches can produce many thousands or even millions of docking poses, and require fast and sensitive scoring functions to distinguish them. Here, we present a novel approach called "EigenHex," which is based on normal mode analyses (NMAs) of a simple elastic network model of protein flexibility. We initially assume that the proteins to be docked are rigid, and we begin by performing conventional soft docking using the Hex polar Fourier correlation algorithm. We then apply a pose-dependent NMA to each of the top 1000 rigid body docking solutions, and we sample and re-score multiple perturbed docking conformations generated from linear combinations of up to 20 eigenvectors using a multi-threaded particle swarm optimization algorithm. When applied to the 63 "rigid body" targets of the Protein Docking Benchmark version 2.0, our results show that sampling and re-scoring from just one to three eigenvectors gives a modest but consistent improvement for these targets. Thus, pose-dependent NMA avoids the need to sample multiple eigenvectors and it offers a promising alternative to combinatorial cross-docking.

Elastic network normal modes provide a basis for protein structure refinement

It is well recognized that thermal motions of atoms in the protein native state, the fluctuations about the minimum of the global free energy, are well reproduced by the simple elastic network models (ENMs) such as the anisotropic network model (ANM). Elastic network models represent protein dynamics as vibrations of a network of nodes (usually represented by positions of the heavy atoms or by the C(α) atoms only for coarse-grained representations) in which the spatially close nodes are connected by harmonic springs. These models provide a reliable representation of the fluctuational dynamics of proteins and RNA, and explain various conformational changes in protein structures including those important for ligand binding. In the present paper, we study the problem of protein structure refinement by analyzing thermal motions of proteins in non-native states. We represent the conformational space close to the native state by a set of decoys generated by the I-TASSER protein structure prediction server utilizing template-free modeling. The protein substates are selected by hierarchical structure clustering. The main finding is that thermal motions for some substates, overlap significantly with the deformations necessary to reach the native state. Additionally, more mobile residues yield higher overlaps with the required deformations than do the less mobile ones. These findings suggest that structural refinement of poorly resolved protein models can be significantly enhanced by reduction of the conformational space to the motions imposed by the dominant normal modes.

FlexE: Using elastic network models to compare models of protein structure.

It is often valuable to compare protein structures to determine how similar they are. Structure comparison methods such as RMSD and GDT-TS are based solely on fixed geometry and do not take into account the intrinsic flexibility or energy landscape of the protein. We propose a method, which we call FlexE, that is based on a simple elastic network model and uses the deformation energy as measure of the similarity between two structures. FlexE can distinguish biologically relevant conformational changes from random changes, while existing geometry-based methods cannot. Additionally, FlexE incorporates the concept of thermal energy, which provides a rational way to determine when two models are "the same". FlexE provides a unique measure of the similarity between protein structures that is complementary to existing methods.

ANM Normal Modes Show the Directions for Protein Structure Refinement

It is well recognized that thermal motions of atoms in the protein native state, which correspond to fluctuations about the minimum of the global free energy, are well reproduced by simple Elastic Network Models (ENMs) such as Anisotropic Network Model (ANM). Elastic Network Models are based on the assumption that all nodes of the network (usually represented, according to the level of coarse graining of the model, by all heavy atoms or by C-alpha atoms only) that are sufficiently close together, based on a predefined cutoff distance, are connected by harmonic or more sophisticated springs. These models provide reliable representation of the fluctuational dynamics of proteins, and indicate the range of various conformational changes in protein structure, e.g. upon ligand binding. the present paper we analyze the problem of protein structure refinement by using thermal motions of proteins in nonnative states. We represent the conformational space close to the native state by a set of decoys generated by the I-TASSER protein structure prediction server utilizing template-free modeling. The protein sub-states were represented by decoys selected from the sets generated by I-TASSER by structure clustering. Based on such selected representatives some dynamical features of nonnative protein states were analyzed in detail and compared. The main finding is that for some of such substates space spanned by their thermal motions overlap significantly with deformation needed to obtain the native state. These findings are used to evaluate their possible applications for protein tertiary structure prediction from amino acid sequence and for structure refinement of low resolution models.

Predicting the order in which contacts are broken during single molecule protein stretching experiments

We combine two methods to enable the prediction of the order in which contacts are broken under external stretching forces in single molecule experiments. These two methods are Gō-like models and elastic network models. The Gō-like models have shown remarkable success in representing many aspects of protein behavior, including the reproduction of experimental data obtained from atomic force microscopy. The simple elastic network models are often used successfully to predict the fluctuations of residues around their mean positions, comparing favorably with the experimentally measured crystallographic B-factors. The behavior of biomolecules under external forces has been demonstrated to depend principally on their elastic properties and the overall shape of their structure. We have studied in detail the muscle protein titin and green fluorescent protein and tested for ten other proteins. First, we stretch the proteins computationally by performing stochastic dynamics simulations with the Gō-like model. We obtain the force-displacement curves and unfolding scenarios of possible mechanical unfolding. We then use the elastic network model to calculate temperature factors (B-factors) and compare the slowest modes of motion for the stretched proteins and compare them with the predicted order of breaking contacts between residues in the Gō-like model. Our results show that a simple Gaussian network model is able to predict contacts that break in the next time stage of stretching. Additionally, we have found that the contact disruption is strictly correlated with the highest force exerted by the backbone on these residues. Our prediction of bond-breaking agrees well with the unfolding scenario obtained with the Gō-like model. We anticipate that this method will be a useful new tool for interpreting stretching experiments.

Protein Structural Variation in Computational Models and Crystallographic Data

Normal mode analysis offers an efficient way of modeling the conformational flexibility of protein structures. Simple models defined by contact topology, known as elastic network models, have been used to model a variety of systems, but the validation is typically limited to individual modes for a single protein. We use anisotropic displacement parameters from crystallography to test the quality of prediction of both the magnitude and directionality of conformational variance. Normal modes from four simple elastic network model potentials and from the CHARMM forcefield are calculated for a data set of 83 diverse, ultrahigh resolution crystal structures. While all five potentials provide good predictions of the magnitude of flexibility, the methods that consider all atoms have a clear edge at prediction of directionality, and the CHARMM potential produces the best agreement. The low-frequency modes from different potentials are similar, but those computed from the CHARMM potential show the greatest difference from the elastic network models. This was illustrated by computing the dynamic correlation matrices from different potentials for a PDZ domain structure. Comparison of normal mode results with anisotropic temperature factors opens the possibility of using ultrahigh resolution crystallographic data as a quantitative measure of molecular flexibility. The comprehensive evaluation demonstrates the costs and benefits of using normal mode potentials of varying complexity. Comparison of the dynamic correlation matrices suggests that a combination of topological and chemical potentials may help identify residues in which chemical forces make large contributions to intramolecular coupling.

Protein Structural Variation in Computational Models and Crystallographic Data

Normal mode analysis offers an efficient way of modeling the conformational flexibility of protein structures. We use anisotropic displacement parameters from crystallography to test the quality of prediction of both the magnitude and directionality of conformational flexibility. Normal modes from four simple elastic network model potentials and from the CHARMM force field are calculated for a data set of 83 diverse, ultrahigh-resolution crystal structures. While all five potentials provide good predictions of the magnitude of flexibility, all-atom potentials have a clear edge at prediction of directionality, and the CHARMM potential has the highest prediction quality. The low-frequency modes from different potentials are similar, but those computed from the CHARMM potential show the greatest difference from the elastic network models. The comprehensive evaluation demonstrates the costs and benefits of using normal mode potentials of varying complexity.

Protein Promiscuity: Drug Resistance and Native Functions—HIV-1 Case

Protein Promiscuity: Drug Resistance and Native Functions—HIV-1 Case

Anisotropy of Fluctuation Dynamics of Proteins with an Elastic Network Model

Fluctuations about the native conformation of proteins have proven to be suitably reproduced with a simple elastic network model, which has shown excellent agreement with a number of different properties for a wide variety of proteins. This scalar model simply investigates the magnitudes of motion of individual residues in the structure. To use the elastic model approach further for developing the details of protein mechanisms, it becomes essential to expand this model to include the added details of the directions of individual residue fluctuations. In this paper a new tool is presented for this purpose and applied to the retinol-binding protein, which indicates enhanced flexibility in the region of entry to the ligand binding site and for the portion of the protein binding to its carrier protein.